It's always a curious thing, that parents say. I don't know why many say that, my mum has said it to me often, and my friends have been told it too. They say not to be committed to one person, and be happy, yet sometimes, the only way you CAN be happy is to BE committed to a certain person. What's the alternative? Having many different partners, as one night stands, and then they'd moan about that! They want you to not be committed to someone, and then they don't want you having multiple partners. So, what do they want? Basically, they don't want their children to grow up. They are losing control. They hate that feeling. So, they try and give advice that prolongs their 'parental' leadership. And you not committing to someone is evidence that you're still 'a kid'. Which is wrong, but maybe an insight as to what it's like being a parent.
Of course, if my girlfriend said to me I have been told not to be committed to you, then I would probably freak out. I wouldn't want her to be potentially seeing other people, or not feeling like I am the one for her. So, I can understand your girlfriends reaction, and I think it was inevitable.
You're doing the right thing. You're building things back up, explaining what happened, so she knows it wasn't your decision but some advice you got that is actually bad advice. You will repair this, because it's clear you both love and care for each other. It might take a little time, but you will do it. I think you will actually be a lot stronger anyway, once this is has been done. It's bringing you closer together. Sometimes, as ironic as it sounds, you have to break up and get back together to realise how important you are to each other. You need that shock to see what life is like without each other.
My advice would be to ask her out again, and get things back on track. You don't want to be without her, and this wasn't your desire anyway, it was bad advice. Tell her you realise now that, although your mum says you don't need to be committed to one person, you know now that you only need one person in your life, and it's her. And you don't ever want to be without her
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The only good thing about breaking up
Is the making up we do after